It is a hard task to construct a general theory of the topological physics
in nonlinear systems because there are many ways to introduce nonlinearity.
It would be necessary to make individual studies of typical nonlinear models
to achieve at a systematic understanding. We studied the dimerized
Toda-lattice model[1]} and a nonlinear mechanical system[2]} in previous works. These models contain the Su-Schrieffer-Heeger
(SSH) model as an essential term. Indeed, these models are reduced to the
dynamical SSH model provided the nonlinear term is ignored, where the
topological number is well defined and the zero-mode edge state emerges in
the topological phase. Then, we carried out numerical analysis to show the
topological physics is valid even in the presence of the nonlinear term. These models have only two phases, the topological phase and the trivial
phase in the phase diagram in the (\(\lambda ,\xi \) ) plane, with \(\lambda \) 
the dimerization parameter and \(\xi \)  the nonlinearity parameter.
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